Question

What is the square root of the fraction 81 over 144?

Answer 1

Hint: In this problem, we have to find the square root of 81 over 144. We can first convert the given statement into a mathematical form to simplify it. We will get a mathematical form as \[\sqrt{\dfrac{81}{144}}\]. We have to analyse the fraction as the numerator 81 and the denominator 144, both are perfect square terms, so we can simplify to its simplest form and then we can find the final answer.

Complete step-by-step solution:
We know that the statement given is,
square root of the fraction 81 over 144’.
We can convert the given statement into a mathematical form to simplify it.
\[\sqrt{\dfrac{81}{144}}\]
We know that the given terms inside the square root in the numerator and the denominator are perfect square terms, we can now write it as,
\[\sqrt{\dfrac{9\times 9}{12\times 12}}=\sqrt{\dfrac{{{9}^{2}}}{{{\left( 12 \right)}^{2}}}}\]
We can now take individual roots for the numerator and the denominator, we get
\[\Rightarrow \dfrac{\sqrt{{{9}^{2}}}}{\sqrt{{{\left( 12 \right)}^{2}}}}\]
We can now simplify the above step by cancelling the square and the square root, we get
\[\Rightarrow \dfrac{9}{12}=\dfrac{3}{4}\]
Therefore, the square root of the fraction 81 over 144 is \[\dfrac{3}{4}\].

Note: We can also simplify the given problem in another method.
We know that the statement given to be simplified is,
square root of the fraction 81 over 144’.
We can convert the given statement into a mathematical form to simplify it.
\[\sqrt{\dfrac{81}{144}}\]
We know that the given terms inside the square root in the numerator and the denominator are perfect square terms, we can now write it as,
\[\sqrt{\dfrac{9\times 9}{12\times 12}}\]
We can now cancel the terms inside the square root, we get
\[\Rightarrow \sqrt{\dfrac{3\times 3}{4\times 4}}=\sqrt{\dfrac{{{3}^{2}}}{{{4}^{2}}}}\]
We can now cancel the root and the square root, we get
\[\Rightarrow \dfrac{3}{4}\]
Therefore, the square root of the fraction 81 over 144 is \[\dfrac{3}{4}\].